Because you received probation, your case is not eligible for expunction. However, once you finish the probation and the statute of limitations has run, you can petition the court to seal your record (call nondisclosure.)
If you have completed all of the requirements of your probation, you can ask your probation officer to ask the judge if you can be early terminated from probation which means that the probation would be over. If the probation officer will not ask the court, then you can hire a lawyer to file a motion for early termination.
I think Cynthia and Shannon may have missed something.
The initial length of a misdemeanor probation in Texas is three years. So if you received three years' probation up front, it wasn't a misdemeanor. (A two-year probation can be extended th three years if you violate your probation.)
You don't specify whether your probation was a deferred adjudication or a regular probation.
If your probation was a deferred adjudication, then you can't get your record expunged, but you may be able to get your record sealed from public view with a petition for nondisclosure at some point—upon termination of the probation if it's really a misdemeanor; five years after termination of the probation if it was actually a felony. The statute of limitations has nothing to do with it.
If it was a regular probation, you can't get your record sealed or expunged.
As Cynthia noted, you may be able to get the probation terminated early.
Actually, a misdemeanor probation (that can be up to 2 years) can be extended for reasons other than violations - such as need for more time to pay restitution. While I was corrected about the time on the waiting to file a petition for non-disclosure, Mr. Bennett's answer is not completely correct.
If you were extended to finish paying, be aware that you must have completed all the terms and conditions of probation to get your probation early terminated. If it was a felony case to begin with, then you will have to wait as Mr. Bennett explained before you can get your record "sealed".
Good luck and sorry for the confusion.